What is the name of the vertex relax algorithm? "slide relax"
One method to do that:

Select all vertices that you want to be smoothed out,
hit CTRL+B to Bevel,
V to bevel vertices instead of edges,
press M until mode Percent is selected,
use the mouse wheel for setting the number of segments you like (an even number let's you keep the original vertices in place, an odd number splits them),
drag the mouse to adjust the bevel,
hit Return or press LMB once you're satisfied with the result.

Of course you can also hit CTRL+B, then Return or LMB to edit the values in the Bevel Properties Menu.
This description applies to the visualization. If that's a top view of e.g. a wall you'd like to smooth, then you don't have to bevel the vertices, but the corresponding, i.e. you can skip step 3.